Question

graph the function ( f(x) = x^2 - 3 ). then use the line tool to draw the line ( x = 3 ) and then use the dot tool to plot the point ( (3, f(3)) ). question help: (\boldsymbol{\text{message instructor}})

Explanation:

Step1: Identify parent function

The parent function is $y=x^2$, a parabola opening upward with vertex at $(0,0)$.

Step2: Apply vertical shift

The given function is $f(x)=x^2 - 3$, which is the parent function shifted down 3 units. Its vertex is at $(0, -3)$.

Step3: Calculate $f(3)$

Substitute $x=3$ into $f(x)$:
$f(3) = 3^2 - 3 = 9 - 3 = 6$
So the point is $(3, 6)$.

Step4: Graph the function

Plot the vertex $(0,-3)$, and other points (e.g., $(-1,-2)$, $(1,-2)$, $(-2,1)$, $(2,1)$) to draw the upward-opening parabola $f(x)=x^2-3$.

Step5: Plot the required point

Mark the point $(3, 6)$ on the graph.

Answer:

• The graph of $f(x)=x^2-3$ is an upward-opening parabola with vertex at $(0, -3)$.
• The plotted point is $(3, 6)$.